The present invention relates to, Inter alia, noise extraction from a signal. The signal may be used, for example, in the generation of images from projection measurements. Examples of images generated from projection measurements include two-dimensional and three-dimensional SAR (synthetic aperture radar) systems, such as that disclosed in U.S. Pat. No. 5,805,098 to McCorkle, hereby incorporated by reference, wherein an aircraft mounted detector array is utilized to take ground radar measurements. Other examples of systems relating to noise extraction from a signal include fault inspection systems using acoustic imaging, submarine sonar for imaging underwater objects, imaging systems for tunnel detection, oil exploration, geological surveys, etc., and medical diagnostic tools such as sonograms, echocardiograms, x-ray CAT (computer-aided tomography) equipment and MRI (magnetic resonance imaging) equipment.
The U.S. Army has been developing low-frequency ultra-wideband systems to detect targets in foliage, explosive devices buried in the ground, moving targets behind walls or barriers (sensing-through-the-wall). Such systems operate in the low-frequency spectrum than spans from under 100 MHz to several GHz in order to have penetration capability while maintaining high image resolution. Therefore, these systems must operate in the low-frequency spectrum that spans from under 100 MHz to several GHz in order to achieve the penetration capability. A critical challenge for ultra-wideband radar is that collected radar information is corrupted in both the time and frequency domain by radio frequency interference (RFI) signals within the operating spectrum of UWB radar, as the signal occupies a wide spectrum that is also shared by radio, TV, cellular phone, wireless networking, amateur radio and other systems. Because of this interference, the received signal contains spectral content that includes many frequency subbands that are corrupted by energy from all other sources. Within these corrupted subbands, the energy of the received signal is much smaller than that from the interference sources, since the interfering signals are essentially large amplitude noise that often masks the underlying radar signals. In the time domain, the signal is very noisy and might be embedded in the noise floor. Except for targets with very large amplitudes, targets may not be detectable in the presence of interference noise. Conventional techniques usually detect the corrupted frequency bands (due to the interference sources) by searching for the spikes in the spectral domain. The fast Fourier transform (FFT) bins that correspond to the contaminated frequency bands are zeroed out. This technique results in severe sidelobes in the time or spatial domain of the output data and imagery due to the sharp transitions (frequency samples with no information) in the frequency domain. In addition, simply suppressing the information in the contaminated frequency bands will reduce the signal-to-noise ratio (SNR) of the received signal.
One noise suppression technique that has been widely employed in practice involves implementing adaptive notch filters (whose notches in the frequency domain correspond to interference noise components) to suppress the energy from interference noise signals. Depending on the nature of interference noise sources, the notch-filter approach generally results in (i) large sidelobes in the time domain of the received signal and (ii) reduced target amplitudes since our transmitted radar signals are UWB and notching partially eliminates the radar signals of interest. It is generally more desirable to extract the interference noise from signal directly in the time domain for best performance. To avoid the side effects of the notch-filter implementation, Timothy Miller, et al., in the publication entitled “RFI Suppression for Ultra Wideband Radar,” IEEE Transactions on Aerospace and Electronic Systems, vol. 33, no. 4, (October 1997) (herein incorporated by reference) proposed an interference noise suppression technique that estimates the noise components and subtracts (in the time domain) the estimated noise signal from the received radar signal. However, the technique requires complete knowledge of the interference sources. The technique is based on the assumption that the interference sources consist of a number of narrowband amplitude modulation (AM) and frequency modulation (FM) channels. This assumption is no longer valid with the current frequency spectrum, in which most of the communications and TV channels are broadcasting using various digital modulation schemes. Within each communications channel, the radio frequency (RF) signal looks like white noise in the time domain with its amplitude and phase quickly varying with respect to time. Thus, it is not practical to use the Miller technique to estimate these RF interference (RFI) components with digital modulation contents. Besides parametric noise modeling, spectral decomposition, and adaptive filtering have also been explored to solve the RFI problem and so far have yielded limited successes. Most can only provide acceptable results with one particular source of RFI.
Of interest are low-frequency ultra-wideband (UWB) radar systems which transmit signals spanning a wide frequency spectrum from under 100 MHz to several GHz, delivering penetration capability while maintaining high image resolution. See, e.g. J. D. Taylor, ed. Ultra-wideband radar technology, CRC press, 2000; B. R. Crowgey, E. J. Rothwell, L. C. Kempel, and E. L. Mokole, “Comparison of UWB short-pulse and stepped-frequency radar systems for imaging through barriers,” Progress In Electromagnetics Research, vol. 110, pp. 403-419, 2010; and S.-E. Hamran. Radar performance of ultra wideband waveforms. INTECH Open Access Publisher, 2010, all of which are incorporated by reference as though fully reproduced herein. For example, the U.S. Army Research Laboratory (ARL) has been developing low-frequency UWB radar systems to detect difficult targets in various applications such as foliage penetration (FOPEN) [9], ground penetration for improvised explosive device (IED) detection (see. H. Nguyen, K. Kappra, D. Wong, R. Kapoor, and J. Sichina, “Mine field detection algorithm utilizing data from an ultrawideband wide-area surveillance radar,” Proc. SPIE Int. Soc. Opt. Eng., vol. 3392, 627, (1998) herein incorporated by reference) and sensing-through-the-wall (STTW) See, L. H. Nguyen, M. Ressler, and J. Sichina, “Sensing through the wall imaging using the Army Research Lab ultra-wideband synchronous impulse reconstuction (UWB SIRE) radar,” Proceedings of SPIE, vol. 6947, 69470B, 2008, herein incorporated by reference. A critical challenge for low-frequency UWB radars is that collected radar information is very susceptible to corruption by radio frequency interference (RFI) signals within the huge operating spectrum since the radar signal spectrum in this case contains significant overlaps with those of radio, TV, cellular phone, wireless networking, amateur radio, etc., resulting in a severely reduced signal-to-noise ratio (SNR) and ultimately reducing the effectiveness of target detection/classification. The observed received radar signal at aperture ith can often be modeled as a linear combination of the true back-scattered radar signal, the RFI signal, and the typical unstructured dense noise with small variance (e.g., atmospheric interference and thermal noise from transmitter/receiver circuits). Since the interference is often dominated by various modulation schemes popular in wireless broadcasting and communication, the received signal contains spectral content that includes many frequency sub-bands that are corrupted by energy from all other RFI sources. Within these corrupted sub-bands, the energy of the received signal can be much smaller than that from the interference sources, since the interfering signals are essentially large amplitude noise that often masks the underlying radar signals. Alternatively, from the time-domain viewpoint, the signal is very noisy and might be embedded in the noise floor. Except for targets with very large amplitudes, targets may not be detectable in the presence of interference noise.
Mitigation of RFI is a notoriously challenging problem due to the dynamic and unpredictable nature of the noise sources, not to mention the strength of the noisy signals. Previous work in this RFI-mitigation area can be classified into two categories: (i) RFI suppression via filtering techniques, where estimated RFI sources are filtered out or suppressed under the noise floor, and (ii) RFI extraction, where RFI components are first identified, estimated, and then subtracted out of the observed signals.
Following the former approach includes notch filtering, sub-band filtering, and/or adaptive filtering techniques, which are popular in practical implementations due to its simplicity. See for example, T. Koutsoudis and L. A. Lovas, “RF interference suppression in ultrawideband radar receivers,” Proc. of the SPIE, Int. Symp. on Algorithms for Synthetic Aperture Radar Imagery II, vol. 2487, pp. 107-118, Orlando, Fla., April (1995); D. O. Carhoun, “Adaptive nulling and spatial spectral estimatin using an iterated principal components decomposition,” Proc. of the International Conference on Acoustics, Speech, and Signal Processing, pp. 3309-3312, Toronto (1991); and H. Subbaram and K. Abend, “Interference suppression via orthogonal projections: a performance analysis,” IEEE Transactions on Antennas and Propagation, vol. 41, pp. 1187-1194, September (1993), all three of which are incorporated by reference as though fully reproduced herein. This simple approach has been widely employed in practice and it typically involves implementing adaptive notch filters (whose notches in the frequency domain correspond to interference noise components) to suppress the energy from interference noise signals. Depending on the nature of interference noise sources, the notch-filter approach generally would result in (i) large sidelobes in the time domain of the received signal and (ii) reduced target amplitudes since our transmitted radar signals are UWB and obviously notching would eliminate partially the radar signals of interest. To preserve the strength of SAR signals and to avoid significant side-lobes, (which leads to severe ringing problems in the final SAR image), it is always more desirable to extract the interference noise from signal directly in the time domain for best performance.
The first effort in the RFI extraction direction is pioneered by T. R. Miller, J. McCorkle, and L. C. Potter, “Radio frequency interference suppression for foliage penetrating radar imaging,” IEEE Trans. on Aerospace and Electronic Systems, vol. 33, pp. 1142-1156, (October 1997), herein incorporated by reference, which proposes to estimate the noise components and subtracts (in the time domain) the estimated noise signal from the received radar signal. However, this early technique requires complete knowledge of the interference sources since it is based on the assumption that the interference sources consist of a number of narrowband amplitude modulation (AM) and frequency modulation (FM) channels. The assumption is no longer valid with the current frequency spectrum, in which most of the communications and TV channels are broadcasting using various digital modulation schemes. Within each communications channel, the radio frequency (RF) signal looks like white noise in the time domain with its amplitude and phase quickly varying with respect to time. Thus, it is not possible to use the Miller technique to estimate these RF interference (RFI) components with digital modulation contents.
More recent techniques that follows the RFI-extraction approach comprise spectral decomposition X.-Y. Wang, W.-D. Yu, X.-Y. Qi and Y. Liu, “RFI suppression in SAR based on approximated spectral decomposition algorithm,” Electronics Letters, vol. 48, (May 2012), herein incorporated by reference, independent component analysis (ICA) F. Zhou, M. Tao, and X. Bai, “Narrow-band interference suppression for SAR based on independent component analysis,” IEEE Trans. on Geoscience and Remote Sensing, vol. 51, pp. 4952-4960, (October 2013) and F. Zhou and M. Tao, “Research on Methods for Narrow-Band Interference Suppression in Synthetic Aperture Radar Data,” IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, vol. 8, no. 7, pp. 3476-3485, (July 2015); and eigen-decompositions as disclosed in C. Yu, Y. Zhang, Z. Dong, and D. Liang, “Eigen-decomposition method for RFI Suppression Applied to SAR data,” in Proc. Of IEEE Int. Conf on Multimedia Technology (ICMT), pp. 1-4, (2010); E. J. Candes and T. Tao, “Near optimal signal recovery from random projections: universal encoding strategies?,” IEEE Trans. on Information Theory, vol. 52, pp. 5406-5425, (December 2006); E. J. Candes and T. Tao, “Decoding by linear programming,” IEEE Trans. on Information Theory, vol. 51, pp. 4203-4215 (December 2005), all of which are hereby incorporated by reference. The main difficulty here is that collected data are already heavily contaminated with RFI. Hence, unless very accurate prior information on RFI sources exists, it is often very difficult to effectively model or estimate (and then separate) RFI component from the desired SAR component. Most of these algorithms can only provide acceptable results with one particular source of RFI and very restrictive assumptions (e.g., very narrow corrupted RFI sub-bands) due various difficulties in modeling complicated RFI noise sources. For instances, several past efforts have taken advantage of the low-rank or narrowband RFI property to extract them via ICA or eigen-decompositions. See, for example. Donoho, “Compressed sensing,” IEEE Trans. on Information Theory, vol. 52, pp. 1289-1306, (April 2006); E. J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. on Information Theory, vol. 52, pp. 489-509, (February 2006); R. Baraniuk, and P. Steeghs, “Compressive radar imaging,” Proc. IEEE Radar Conference, Waltham, pp. 128˜133, (April 2007); M. Herman and T. Strohmer, “Compressed sensing radar,” Proc. IEEE Acoustics, Speech and Signal Processing, pp. 1509-1512, (May 2008), all of which are incorporated by reference. However, these principal-component-based techniques heavily depend on the quality of the orthogonal subspaces and cannot distinguish signal-versus-noise if they happen to have the same power within the same subspace.
The recently emerging theory of compressed sensing (see for example, L. C. Potter, E. Ertin, J. T. Parker, and M. Cetin. “Sparsity and compressed sensing in radar imaging.” Proceedings of the IEEE 98, no. 6, pp. 1006-1020, (June 2010)) stimulates numerous investigations on the applicability of sparsity in radar imaging. See for example, L. H. Nguyen and T. D. Tran, “Robust and adaptive extraction of RFI signals from ultra-wideband radar data,” IEEE Int. Geoscience and Remote Sensing Symposium (IGARSS), pp. 7137-7140, (July 2012), L. H. Nguyen, T. D. Tran, and T. Do, “Sparse models and sparse recovery for ultra-wideband SAR applications,” IEEE Trans. on Aerospace and Electronic Systems, vol. 50, no. 2, pp. 940-958, (February 2014); L. H. Nguyen and T. D. Tran, “Method and system for removal of noise in signal,” U.S. Pat. No. 9,172,476. (October 2015); L. H. Nguyen and T. D. Tran, “Estimation and extraction of radio-frequency interference from ultra-wideband radar signals,” IEEE Int. Geoscience and Remote Sensing Symposium (IGARSS), pp. 2848-2851, (July 2015); L. H. Nguyen and T. D. Tran, “Efficient and robust RFI extraction via sparse recovery,” IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, to appear in future, (2016) L. H. Nguyen and T. D. Tran, “Method and system for estimation and extraction of interference noise from signals,” U.S. patent application Ser. No. 14/452,902, filed Aug. 6, 2014, now U.S. Pat. No. 9,363,024; all of which are herein incorporated by reference. Most sparsity-based approaches tend to focus on obtaining sparse scenes; hence, they involve computationally expensive optimization algorithms with the image formation step embedded right within the main iterative loop. As a result, these algorithms are not directly applicable to UWB high-resolution SAR applications, where sampling rates are often in the GHz range, scene resolution is usually in the sub-meter range, and hundreds of data records need to be collected and processed every second.
Previous attempt in solving the RFI problem follows the RFI-extraction approach via sparse recovery and requires prior knowledge of the SAR system or the RFI sources or both. Our very first effort requires a priori information on both SAR and RFI components described in U.S. Pat. No. 9,172,476. This technique has one significant drawback: the radar system has to continuously monitor the surrounding environment in order to build a representation dictionary for the interference sources. We have suggested turning the radar transmitter off occasionally while leaving the receiver on as a simple and quick solution. This way, whenever the radar system is in the sniffing stage, i.e., the transmitter is turned off, the receiver would collect only the vital information on the interference (since there is no radar signal present, what we sense must be pure interference). However, even this simple “sniffing” solution (i) increases the complexity of the system control and (ii) reduces the system's effective pulse repetition frequency (PRF). Obviously, if we desire to capture the interference characteristics accurately, then we would need to increase the sniffing frequency and the system's PRF would decrease significantly. On the other hand, if we try to minimize the amount of sniffing, then the interference modeling will not be as precise, rendering our proposed solution to be much less effective.
More recently, a sparsity-driven technique was developed that directly estimates the interference noise components in the time domain and extracts them from radar data U.S. patent application Ser. No. 14/452,902, filed Aug. 6, 2014, now U.S. Pat. No. 9,363,024. The first-advantage of this technique is that the time-domain extraction of RFI noise does not result in (i) large side-lobes in the time domain of the received signal and (ii) reduced target amplitudes. The second advantage is that it is completely adaptive with the changing environment and does not assume any knowledge (amplitude, frequency band, modulation scheme, etc.) of the interference sources. The invented technique simultaneously estimates (i) the radar signal embedded in interference noise with large amplitudes and (ii) the interference noise signal via a joint-sparse-recovery framework. However, the effectiveness of this technique still depends on the quality of the RFI estimation step, particularly when the RFI is highly non-stationary over time and aperture positions. Also, this estimation stage adds additional level of complexity to the overall radar system.